ELASTIC-PLASTIC BEAM-COLUMN FEM MODEL WITH FIBER ELEMENTS EVALUATING SHEAR DEFORMATION

Abstract

This paper proposes a new beam-column FEM which consists of several fiber elements considering shear deformation. The distribution of normal strain obeys Bernouli-Euler hypothesis. The distribution of shear strain is suggested here to be Equation (17). The proposed distribution is expressed by the product of distribution of shear strain and shear deformation angle at the elastic state. The formulation is accomplished based on the incremental perturbation method. Normal stress-strain relation and shear stress-strain relation in the fiber element are supposed here to obey each different consistent law independently. The new generalized displacement vectors with a shear deformation angle and the corresponding force vectors are defined here as shown in Eqs. (2) and (3). In order to analyze combined non-linear problem, the moving coordinate system in the previous beam-column FEM known as FERT is adopted here. The matrix of coordinates transformation is conducted here. Also, the formularization described in chapter 2 is developed by the incremental perturbation theory. The verification of the proposed numerical method named FERTs-P is carried out for the problem of elastic beam and elastic-plastic beam. Also the simulation of the steel beam experiment and the frame experiment with a shear panel are done by the FERTs-P. The section quantities consisted by fiber elements are set up to be equivalent to area, moment of inertia and plastic section modules. The tri-linear models are adopted here as the relation of shear stress-strain and that of normal stress-strain. The main observations are as follows: (1) The ratios of shear deformation to bending deformation in elastic beams are almost coincident with theoretical values due to Timoshenko beam. (2) The numerical results by FERTs-P are relatively good predictions for the experimental load-deflection curves of beams and frame yielding at shear. (3) The FERTs-P is effective to predict elastic-plastic bending behavior. In spite of bold modeling, this numerical method may be expected considerably. Moreover the consistent law in shear stress-strain relation will be considered.